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Explain the divisibility rules of 7 and 9.
Divisibility rule for 7:
• First double the last digit of the number.
• Then subtract it from the remaining number.
• If the result is divisible by 7, then the original number will also be divisible by 7.
For example: Let’s check if 623 is divisible by 7 or not.
• First double the last digit of the number ($3 \times 2 = 6$).
• Then subtract it from the remaining number ($62 – 6 = 56$).
• We know that 56 is divisible by 7ie, $\frac{56}{7} \ =8$, then the original number (623) will also be divisible by 7 ie, $\frac{623}{7} \ =89$.
Divisibility rule for 9:The rule for divisibility by 9 is similar to divisibility rule for 3. That is, if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.
For example,
64654,
The sum of the digits ($6+4+6+5+4$) is 25, which is not divisible by 9, hence 64654 is not divisible by 9.
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